Practitioners of the art of scanning tunneling microscopy generally use either Integral, Integral with Proportion, or Integral-Proportion-Derivative (collectively “PID”) methodologies for feedback control as the tip electrode approaches the sample electrode to establish quantum tunneling and to maintain an approximately constant tunneling current after tunneling is established in a scanning tunneling microscope (STM) [D. Jeon and R. F. Willis, “Feedback system response in a scanning tunneling microscope,” Rev. Sci. Instrum. Vol. 62, June 1991, pp. 1650-1651.]. Variants of PID feedback control, including one or more from the group Proportion, Integral, and Derivative, are appropriate in many applications once quantum tunneling has been established, such as in temperature control where a time-dependent error signal is continuously present. However, in scanning tunneling microscopy there is no measurable tunneling current until the tip is less than 1 nm from the sample, so without adequate control a moving tip may continue its motion and make contact in what is called “tip-crash” because the error signal maintains a value of 100% until the point where action must be taken immediately to prevent catastrophic failure. Tip crash ruins the tip and sample for nanoscale measurements. Many papers have been published showing atomic resolution with highly oriented pyrolytic graphite (HOPG) using different types of scanning tunneling microscopes that were operated in air. However, other measurements made under these conditions show that the giant corrugations seen in these images are artifacts caused by the pressure of the tip which is in direct contact with the sample [H. J. Mamin, E. Ganz, D. W. Abraham, R. E. Thomson and J. Clarke, “Contamination-mediated deformation of graphite by the scanning tunneling microscope,” Phys. Rev. B, Vol. 34, December 1986, pp. 9015-9018.]. Furthermore, with tip-sample contact instead of quantum tunneling, there is also atomic resolution when the PID feedback control is disabled [R. J. Colton, S. M. Baker, R. J. Driscoll, M. G. Youngquist and J. D. Baldeschwieler, “Imaging graphite in air by scanning tunneling microscopy: role of the tip,” J. Vac. Sci. technol. A, Vol. 6, March/April 1988, pp. 349-353.]. For quantitative research on laser-assisted tunneling, including the generation of a microwave frequency comb by optical rectification in a tunneling junction, it is essential to operate the STM in the tunneling mode because there is no microwave signal with tip-sample contact [M. J. Hagmann, F. S. Stenger, and A. Yarotski, “Linewidth of the harmonics in a microwave frequency comb generated by focusing a mode-locked ultrafast laser on a tunneling junction,” J. Appl. Phys. Vol. 114, 2013, 223107]. While a rudimentary image can be obtained when the tip and sample are in contact, there would be no microwave frequency comb. Likewise, measurements of barrier height are totally meaningless when the tip and sample are in contact [J. M. Soler, A. M. Baro, N. Garcia and H. Rohrer, “Interatomic forces in scanning tunneling microscopy: giant corrugations of the graphite surface,” Phys. Rev. Lett. Vol. 57, July 1986, pp. 444-447].
Typically, the derivative function is not used because it creates instability by accentuating the high-frequency noise in the current. Proportion methodology during approach is of little value because the RMS current (noise) obscures the difference between current when the tip is at one distance from the sample as opposed to that at a second distance. Furthermore, Integral methodology, which is frequently used by itself for feedback control in an STM, accumulates a significant error, called “integral windup,” during tip approach. This integral windup is a result of the integration function being from a time T=0 s to the time the measurement is taken. This long time period creates data bias which interferes with the response that is essential to prevent tip-crash. Digital signal processors have been used to provide a faster response; but, this does not solve the problem of instability in the feedback control.
An analytic model of one embodiment of the present invention includes simulation of the effects of drift and noise on the current measured in a STM. The algorithm described herein was developed and the digital feedback control described using this algorithm is unusually stable. In simulations where Proportion and/or Integral methodologies are added to the algorithm, the stability of the feedback control is decreased.
The present invention represents a departure from the prior art in that the control methodology of the present invention allows for precise and stable relative positioning of tip and sample electrodes in an STM without the risk of tip-crash. The methodology also has the unexpected benefit of prolonging the usefulness of tip electrodes, including for continuous tunneling over multiple days. It is hypothesized that the stability of the algorithm not only prevents destruction caused by tip crash but also promotes continual cleaning of oxidized deposits off of said electrodes because the electric field is more nearly constant.